Estimates of Number of Undiscovered Deposits of Gold,Silver, Copper,Lead, and Zinc in the United States

Estimates of the number of undiscovered deposits offer a unique perspective on the nation's undiscovered mineral resources. As part of the 1998 assessment of undiscovered deposits of gold, silver, copper, lead, and zinc, estimates of the number of deposits were made for 305 of the 447 permissive tracts delineated in 19 assessment regions of the country. By aggregating number of undiscovered deposits by deposit type and by assessment region, a picture of the nation's undiscovered resources has emerged. For the nation as a whole, the mean estimate for the number of undiscovered deposits is 950. There is a 90% chance there are at least 747 undiscovered deposits and a 10% chance there are as many as 1,160 undiscovered deposits. For Alaska, the mean estimate for the number of undiscovered deposits is 281. There is a 90% chance there are at least 168 undiscovered deposits and a 10% chance there are as many as 402 undiscovered deposits. Assuming that the majority of deposits used to create the grade and tonnage models that formed the basis for estimating the number of undiscovered deposits are significant deposits, there remain about as many undiscovered deposits as have already been discovered. Consideration of the number of undiscovered deposits as part of national assessments carried out on a recurring basis serves as a leading indicator of the nation's total mineral resources.     

The study of the undiscovered mineral resources of the Tongass National Forest and adjacent lands,Southeastern Alaska

The quantitative probabilistic assessment of the undiscovered mineral resources of the 17.1-million-acre Tongass National Forest (the largest in the United States) and its adjacent lands is a nonaggregated, mineral-resource-tract-oriented assessment designed for land-planning purposes. As such, it includes the renewed use of gross-in-place values (GIPV's) in dollars of the estimated amounts of metal contained in the undiscovered resources as a measure for land-use planning.Southeastern Alaska is geologically complex and contains a wide variety of known mineral deposits, some of which have produced important amounts of metals during the past 100 years. Regional geological, economic geological, geochemical, geophysical, and mineral exploration history information for the region was integrated to define 124 tracts likely to contain undiscovered mineral resources. Some tracts were judged to contain more than one type of mineral deposit. Each type of deposit may contain one or more metallic elements of economic interest. For tracts where information was sufficient, the minimum number of as-yet-undiscovered deposits of each type was estimated at probability levels of 0.95, 0.90, 0.50, 0.10, and 0.05.The undiscovered mineral resources of the individual tracts were estimated using the U.S. Geological Survey's MARK3 mineral-resource endowment simulator; those estimates were used to calculate GIPV's for the individual tracts. Those GIPV's were aggregated to estimate the value of the undiscovered mineral resources of southeastern Alaska. The aggregated GIPV of the estimates is $40.9 billion.Analysis of this study indicates that (1) there is only a crude positive correlation between the size of individual tracts and their mean GIPV's: and (2) the number of mineral-deposit types in a tract does not dominate the GIPV's of the tracts, but the inferred presence of synorogenic-synvolcanic nickel-copper, porphyry copper skarn-related, iron skarn, and porphyry copper-molybdenum deposits does. The influence of this study on the U.S. Forest Service planning process is yet to be determined.     

Economic Filters Applied to Quantitative Mineral Resource Simulations

The U.S. Geological Survey has developed a technique that allows mineral resource experts to apply economic filters to estimates of undiscovered mineral resources. This technique builds on previous work that developed quantitative methods for mineral resource assessments. A Monte-Carlo calculation uses mineral deposit models to estimate commodity grades and tonnages of undiscovered deposits. The results then are analyzed using simple estimates of capital expenditures and daily operating costs for a mine and associated mill. The daily operating costs and the value of the ore are used to calculate the net present value of the deposit, which is compared to the capital expenditures to determine whether the deposit is economic. Repetition of these calculations for many deposits produces a table that can be interpreted in terms of the probability of there being deposits that have anet present value exceeding some specified amount. Sample calculations indicate that applying economic filters to simulated mineral resources might change the perception of the results compared to presenting the calculations in terms of the expected mean gross-in-place value of the minerals.     

Map Scale Effects on Estimating the Number of Undiscovered Mineral Deposits

Estimates of numbers of undiscovered mineral deposits, fundamental to assessing mineral resources, are affected by map scale. Where consistently defined deposits of a particular type are estimated, spatial and frequency distributions of deposits are linked in that some frequency distributions can be generated by processes randomly in space whereas others are generated by processes suggesting clustering in space. Possible spatial distributions of mineral deposits and their related frequency distributions are affected by map scale and associated inclusions of non-permissive or covered geological settings. More generalized map scales are more likely to cause inclusion of geologic settings that are not really permissive for the deposit type, or that include unreported cover over permissive areas, resulting in the appearance of deposit clustering. Thus, overly generalized map scales can cause deposits to appear clustered. We propose a model that captures the effects of map scale and the related inclusion of non-permissive geologic settings on numbers of deposits estimates, the zero-inflated Poisson distribution. Effects of map scale as represented by the zero-inflated Poisson distribution suggest that the appearance of deposit clustering should diminish as mapping becomes more detailed because the number of inflated zeros would decrease with more detailed maps. Based on observed worldwide relationships between map scale and areas permissive for deposit types, mapping at a scale with twice the detail should cut permissive area size of a porphyry copper tract to 29% and a volcanic-hosted massive sulfide tract to 50% of their original sizes. Thus some direct benefits of mapping an area at a more detailed scale are indicated by significant reductions in areas permissive for deposit types, increased deposit density and, as a consequence, reduced uncertainty in the estimate of number of undiscovered deposits. Exploration enterprises benefit from reduced areas requiring detailed and expensive exploration, and land-use planners benefit from reduced areas of concern.     

The deposit size frequency method for estimating undiscovered uranium deposits

The deposit size frequency (DSF) method has been developed as a generalization of the method that was used in the National Uranium Resource Evaluation (NURE) program to estimate the uranium endowment of the United States. The DSF method overcomes difficulties encountered during the NURE program when geologists were asked to provide subjective estimates of (1) the endowed fraction of an area judged favorable (factorF) for the occurrence of undiscovered uranium deposits and (2) the tons of endowed rock per unit area (factorT) within the endowed fraction of the favorable area. Because the magnitudes of factorsF andT were unfamiliar to nearly all of the geologists, most geologists responded by estimating the number of undiscovered deposits likely to occur within the favorable area and the average size of these deposits. The DSF method combines factorsF andT into a single factor (F·T) that represents the tons of endowed rock per unit area of the undiscovered deposits within the favorable area. FactorF·T, provided by the geologist, is the estimated number of undiscovered deposits per unit area in each of a number of specified deposit-size classes. The number of deposit-size classes and the size interval of each class are based on the data collected from the deposits in known (control) areas. The DSF method affords greater latitude in making subjective estimates than the NURE method and emphasizes more of the everyday experience of exploration geologists. Using the DSF method, new assessments have been made for the young, organic-rich surficial uranium deposits in Washington and idaho and for the solution-collapse breccia pipe uranium deposits in the Grand Canyon region in Arizona and adjacent Utah.     

Geologic risk, economic assessment, and optimal decision making of petroleum plays in the Bohaiwan Basin, northern China

A system of play (trap) assessment based on the analysis of geological characteristics of five different types of petroleum plays in the Bohaiwan Basin, northern China, is proposed. The system makes use of conditional probability, fuzzy logic, and Monte Carlo simulation to assess geologic risk for estimating the undiscovered petroleum resources in a region. Combining the estimates of undiscovered resources with the subsequent economic evaluation of discovered resources by using techniques of optimization, the expected monetary value can be estimated to determine the overall benefits of an investment. A software program has been developed to carry out the calculations.     

Using PETRIMES to estimate mercury deposits in California

In this article, we examine the use of an unconventional procedure, PETRIMES, to estimate mineral resources of mercury deposits in California. The study, which is based on the nonparametric discovery process model and Q-Q plots, suggests that a lognormal distribution is appropriate for the mercury deposits in California. The results of the assessment are summarized as follows: (1) the total number of mercury deposits in the population is approximately 165; (2) the median value of the largest undiscovered deposit size is 487 flasks; (3) the mean of the remaining mercury potential is 2,500 flasks; and (4) the population resource ranges from 1,040,000 to 4,300,000 flasks (at a 0.9 probability level).     

Worldwide Estimates of Deep Natural Gas Resources Based on the U.S. Geological Survey World Petroleum Assessment 2000

The U.S. Geological Survey recently assessed undiscovered conventional gas and oil resources in eight regions of the world outside the U.S. The resources assessed were those estimated to have the potential to be added to reserves within the next thirty years. This study is a worldwide analysis of the estimated volumes and distribution of deep (>4.5 km or about 15,000 ft), undiscovered conventional natural gas resources based on this assessment. Two hundred forty-six assessment units in 128 priority geologic provinces, 96 countries, and two jointly held areas were assessed using a probabilistic Total Petroleum System approach. Priority geologic provinces were selected from a ranking of 937 provinces worldwide. The U.S. Geological Survey World Petroleum Assessment Team did not assess undiscovered petroleum resources in the U.S. For this report, mean estimated volumes of deep conventional undiscovered gas resources in the U.S. are taken from estimates of 101 deep plays (out of a total of 550 conventional plays in the U.S.) from the U.S. Geological Survey's 1995 National Assessment of Oil and Gas Resources. A probabilistic method was designed to subdivide gas resources into depth slices using a median-based triangular probability distribution as a model for drilling depth to estimate the percentages of estimated gas resources below various depths. For both the World Petroleum Assessment 2000 and the 1995 National Assessment of Oil and Gas Resources, minimum, median, and maximum depths were assigned to each assessment unit and play; these depths were used in our analysis. Two-hundred seventy-four deep assessment units and plays in 124 petroleum provinces were identified for the U.S. and the world. These assessment units and plays contain a mean undiscovered conventional gas resource of 844 trillion cubic ft (Tcf) occuring at depths below 4.5 km. The deep undiscovered conventional gas resource (844 Tcf) is about 17% of the total world gas resource (4,928 Tcf) based on the provinces assessed and includes a mean estimate of 259 Tcf of U.S. gas from the U.S. 1995 National Assessment. Of the eight regions, the Former Soviet Union (Region 1) contains the largest estimated volume of undiscovered deep gas with a mean resource of343 Tcf.     

Rank-Size Statistical Assessments of Undiscovered Gold Endowment in the Bendigo and Stawell Zones (Victoria) and the Mossman Orogen (Queensland), Australia: Comparison with Three-Part Assessment Results

The Bendigo and Stawell zones in Victoria and the Mossman Orogen in north Queensland host numerous orogenic gold deposits and are likely to contain significant undiscovered gold resources. This paper discusses applications of Zipf’s law to estimate the scale of residual gold endowment in each of the regions. Testing various plausible scenarios on whether or not the largest deposit in each region has been discovered and its endowment adequately evaluated provided some measure of uncertainty of assessment results. The Bendigo and Stawell zones are estimated to host 12 undiscovered ore fields with >31 t (1 Moz) of contained gold and another 35 undiscovered ore fields with >10 t (0.32 Moz) of gold, containing in total 1600 t (51 Moz) of gold. The total residual orogenic gold endowment of the Mossman Orogen is estimated to be between 3 and 30 t of gold, contained in extensions of known deposits and up to six significant undiscovered gold ore fields each containing >1 t of gold. These estimates are comparable to results of recent three-part quantitative mineral resource assessments for those areas.     

Estimation of undiscovered deposits in quantitative mineral resource assessments—examples from Venezuela and Puerto Rico

Quantitative mineral resource assessments used by the United States Geological Survey are based on deposit models. These assessments consist of three parts: (1) selecting appropriate deposit models and delineating on maps areas permissive for each type of deposit; (2) constructing a grade-tonnage model for each deposit model; and (3) estimating the number of undiscovered deposits of each type. In this article, I focus on the estimation of undiscovered deposits using two methods: the deposit density method and the target counting method.In the deposit density method, estimates are made by analogy with well-explored areas that are geologically similar to the study area and that contain a known density of deposits per unit area. The deposit density method is useful for regions where there is little or no data. This method was used to estimate undiscovered low-sulfide gold-quartz vein deposits in Venezuela.Estimates can also be made by counting targets such as mineral occurrences, geophysical or geochemical anomalies, or exploration plays and by assigning to each target a probability that it represents an undiscovered deposit that is a member of the grade-tonnage distribution. This method is useful in areas where detailed geological, geophysical, geochemical, and mineral occurrence data exist. Using this method, porphyry copper-gold deposits were estimated in Puerto Rico.     

Conditional estimates of the number of podiform chromite deposits

A desirable guide for estimating the number of undiscovered mineral deposits is the number of known deposits per unit area from another well-explored permissive terrain. An analysis of the distribution of 805 podiform chromite deposits among ultramafic rocks in 12 subareas of Oregon and 27 counties of California is used to examine and extend this guide. The average number of deposits in this sample of 39 areas is 0.225 deposits per km² of ultramafic rock; the frequency distribution is significantly skewed to the right. Probabilistic estimates can be made by using the observation that the lognormal distribution fits the distribution of deposits per unit area. A further improvement in the estimates is available by using the relationship between the area of ultramafic rock and the number of deposits.The number (N) of exposed podiform chromite deposits can be estimated by the following relationship: log₁₀(N)=–0.194+0.577 log₁₀(area of ultramafic rock). The slope is significantly different from both 0.0 and 1.0. Because the slope is less than 1.0, the ratio of deposits to area of permissive rock is a biased estimator when the area of ultramafic rock is different from the median 93 km². Unbiased estimates of the number of podiform chromite deposits can be made with the regression equation and 80 percent confidence limits presented herein.     

Quantitative assessment of future development of cooper/silver resources in the Kootenai National Forest,Idaho/Montana: Part I—Estimation of the copper and silver endowments

Faced with an ever-increasing diversity of demand for the use of public lands, managers and planners are turning more often to a multiple-use approach to meet those demands. This approach requires the uses to be mutually compatible and to utilize the more valuable attributes or resource values of the land. Therefore, it is imperative that planners be provided with all available information on attribute and resource values in a timely fashion and in a format that facilitates a comparative evaluation.The Kootenai National Forest administration enlisted the U.S. Geological Survey and U.S. Bureau of Mines to perform a quantitative assessment of future copper/silver production potential within the forest from sediment-hosted copper deposits in the Revett Formation that are similar to those being mined at the Troy Mine near Spar Lake. The U.S. Geological Survey employed a quantitative assessment technique that compared the favorable host terrane in the Kootenai area with worldwide examples of known sediment-hosted copper deposits. The assessment produced probabilistic estimates of the number of undiscovered deposits that may be present in the area and of the copper and silver endowment that might be contained in them.Results of the assessment suggest that the copper/silver deposit potential is highest in the southwestern one-third of the forest. In this area there is an estimated 50 percent probability of at least 50 additional deposits occurring mostly within approximately 260,000 acres where the Revett Formation is thought to be present in the subsurface at depths of less than 1,500 meters. A Monte Carlo type simulation using data on the grade and tonnage characteristics of other known silver-rich, sediment-hosted copper deposits predicts a 50 percent probability that these undiscovered deposits will contain at least 19 million tonnes of copper and 100,000 tonnes of silver. Combined with endowments estimated for identified, but not thoroughly explored deposits, and deposits that might also occur in the remaining area of the forest, the endowment potential increases to 23 million tonnes of copper and 190,000 tonnes of silver.     

Correlation between assessments of undiscovered oil and gas resources

There is an inbuilt correlation between estimated quantities of oil and gas produced by probabilistic assessments of undiscovered oil and gas resources. Correlation between assessed quantities of oil and gas occurs at every level, whether prospects, plays, basins, continents, or the world. Providing that the oil and gas are assessed in the same run of the computer program, the correlation can be calculated using the paired values of the undiscovered oil and gas volumes calculated in each of the Monte Carlo simulations. It can be seen in the shape and density of a point plot of these paired values. Alternatively, the correlation can be calculated theoretically using an equation written in terms of the data input to the assessment program. These commonly include distributions for the number of accumulations (N), the success rate (s), the accumulation sizes (V), an oil to gas conversion factor, and a proportion of oil to oil plus gas (P _OOG). The cause of the correlation is investigated and explained using point plots and equations for a variety of input distributions. The shape and density of each plot are determined by the pattern of the numbers of oil and gas accumulations, the sizes of the accumulations, and the proportions of oil to oil plus gas. The correlation is caused by the dispersion or spread of the input distributions. It may be positive or negative, tending toward positive as the dispersions ofN, s, andV increase and the dispersion ofP _OOG decreases. The correlation indicates that there is a relationship between the undiscovered oil and gas resources that may be described by fitting a linear regression to a plot of the paired values of the total oil and gas resources. The relationship should be quoted as part of the assessment and might be used to make a better estimate of the value of the undiscovered resources.     

Guiding Principles of USGS Methodology for Assessment of Undiscovered Conventional Oil and Gas Resources

During the last 30 years, the methodology for assessment of undiscovered conventional oil and gas resources used by the Geological Survey has undergone considerable change. This evolution has been based on five major principles. First, the U.S. Geological Survey has responsibility for a wide range of U.S. and world assessments and requires a robust methodology suitable for immaturely explored as well as maturely explored areas. Second, the assessments should be based on as comprehensive a set of geological and exploration history data as possible. Third, the perils of methods that solely use statistical methods without geological analysis are recognized. Fourth, the methodology and course of the assessment should be documented as transparently as possible, within the limits imposed by the inevitable use of subjective judgement. Fifth, the multiple uses of the assessments require a continuing effort to provide the documentation in such ways as to increase utility to the many types of users. Undiscovered conventional oil and gas resources are those recoverable volumes in undiscovered, discrete, conventional structural or stratigraphic traps. The USGS 2000 methodology for these resources is based on a framework of assessing numbers and sizes of undiscovered oil and gas accumulations and the associated risks. The input is standardized on a form termed the Seventh Approximation Data Form for Conventional Assessment Units. Volumes of resource are then calculated using a Monte Carlo program named Emc2, but an alternative analytic (non-Monte Carlo) program named ASSESS also can be used. The resource assessment methodology continues to change. Accumulation-size distributions are being examined to determine how sensitive the results are to size-distribution assumptions. The resource assessment output is changing to provide better applicability for economic analysis. The separate methodology for assessing continuous (unconventional) resources also has been evolving. Further studies of the relationship between geologic models of conventional and continuous resources will likely impact the respective resource assessment methodologies.     

A Framework for Expert Judgment to Assess Oil and Gas Resources

In frontier areas, where well data are sparse, many organizations have used expert judgment to estimate undiscovered resources. In this process, several important issues arise. How should the knowledge be elicited? At what level of aggregation (geologic process model, play, petroleum system, country, etc.) should the assessment be performed? How and at what stage of the assessment process should feedback be given to assessors? Is independent replication of estimates possible? How are issues of dependency treated? When and how should uncertainty be specified? The context for this presentation will be the methodology used in the US Geological Survey's 1998 1002-Arctic National Wildlife Refuge assessment of oil and gas resources.

     

Basic concepts in three-part quantitative assessments of undiscovered mineral resources

Since 1975, mineral resource assessments have been made for over 27 areas covering 5×10⁶ km² at various scales using what is now called the three-part form of quantitative assessment. In these assessments, (1) areas are delineated according to the types of deposits permitted by the geology,(2) the amount of metal and some ore characteristics are estimated using grade and tonnage models, and (3) the number of undiscovered deposits of each type is estimated.Permissive boundaries are drawn for one or more deposit types such that the probability of a deposit lying outside the boundary is negligible, that is, less than 1 in 100,000 to 1,000,000.     

Probabilistic Estimates of Number of Undiscovered Deposits and Their Total Tonnages in Permissive Tracts Using Deposit Densities

Empirical evidence indicates that processes affecting number and quantity of resources in geologic settings are very general across deposit types. Sizes of permissive tracts that geologically could contain the deposits are excellent predictors of numbers of deposits. In addition, total ore tonnage of mineral deposits of a particular type in a tract is proportional to the type’s median tonnage in a tract. Regressions using size of permissive tracts and median tonnage allow estimation of number of deposits and of total tonnage of mineralization. These powerful estimators, based on 10 different deposit types from 109 permissive worldwide control tracts, generalize across deposit types. Estimates of number of deposits and of total tonnage of mineral deposits are made by regressing permissive area, and mean (in logs) tons in deposits of the type, against number of deposits and total tonnage of deposits in the tract for the 50th percentile estimates. The regression equations (R ² = 0.91 and 0.95) can be used for all deposit types just by inserting logarithmic values of permissive area in square kilometers, and mean tons in deposits in millions of metric tons. The regression equations provide estimates at the 50th percentile, and other equations are provided for 90% confidence limits for lower estimates and 10% confidence limits for upper estimates of number of deposits and total tonnage. Equations for these percentile estimates along with expected value estimates are presented here along with comparisons with independent expert estimates. Also provided are the equations for correcting for the known well-explored deposits in a tract. These deposit-density models require internally consistent grade and tonnage models and delineations for arriving at unbiased estimates.     

Bayesian Discovery Process Modeling of the Lower and Middle Jurassic Play of the Halten Terrace,Offshore Norway,as Compared with the Previous Modeling

A Bayesian version of the discovery process model was applied to the pre-rift Lower and Middle Jurassic play of the Halten Terrace, Mid-Norway. The Bayesian approach estimates the lognormal parameters, the discoverability parameter, and the distribution of sizes of the undiscovered fields as well as the play potential, conditioned on a discovery sequence averaging for all possible prior choices weighted by their likelihood. This approach avoids the problem of having to make arbitrary choices for the parameters. The estimates of parameters and play potential based upon the present methodology compares well with previous estimates, if the play is divided into two sub-plays representing the overpressured and normally pressured zones. These sub-plays have been estimated independently and aggregated in order to get the total undiscovered resource potential. This study estimates that the expected remaining play potential is 100 × 10⁶Sm³ o.e., about 9% of the total resources in the play. There is however a 90% chance that the remaining potential ranges from 13 to 282× 10⁶ Sm³ o.e. and a 5% possibility of exceeding this value.     

Annotated bibliography of methodology for assessment of undiscovered oil and gas resources

An annotated bibliography of methodology of assessment of undiscovered oil and gas resources is presented as a useful reference for those engaged in resource assessment. The articles that are included deal only with quantitative assessment of undiscovered or inferred resources. the articles in this bibliography are classified largely according to the major assessment method that was applied in each situation. Major assessment methods include areal and volumetric yield methods, field size distributions, historical extrapolation, deposit modeling, organic geochemical mass balance methods, and direct expert assessment. Other categories include mathematical tools, reserve growth/confirmation, quantitative characterization of undiscovered resources, and general topics. For the purpose of future updates, we solicit contributions of articles that may have been missed in the preparation of this bibliography.